数学物理方程-第4讲（2.2-2.3）.doc

文档介绍：Mathematical Physics Equations
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2

w w
u u
2
° w w =<<>
axl t
0 0
2
t x
w u
° ® = = +
u hu
| 0, ( ) | 0
xx lx
=w =
0
° =
u M x
| ( )
t= 0
°
¯
=
2 "()(),
X xT t
w w
xt
w u


u(x,t) = tX (x)T ()
= X xT t
()'()

X (x)T '(t) = 2 ta X "(x)T ()
X xT t
"() '()
= 2
X xa T t
() ()
= - λ

X xT t
"() '()
=
2
X x
() ()
a T t
2
T ta T t
'() () 0
+ =
ë
X xX x
"() () 0
+ =
ë

>0 =2
2 2
Tt a T t
'() () 0
+ =
â